Optimal model predictive control solution approximation using Takagi Sugeno for linear and a class of nonlinear systems

The universal approximation property of Takagi-Sugeno fuzzy systems is exploited here to build a fuzzy approximation of the optimal solution of linear and nonlinear model predictive control (MPC). The nonlinear systems considered are affine in the control law. The fuzzy approximator introduced presents some properties not generally shown by the previous approximators. In particular it is constituted by a set of state feedback control laws which are merged to obtain the final nonlinear control law. The constructed control law is very similar to the explicit solution of the linear MPC. The a posteriori stability is analysed based on a novel theoretical test previously published for both the linear and nonlinear MPC. Examples treated in the simulation part have shown the prompt and the good results which prove the effectiveness of the developed control strategy.